I suspect the answer lies primarily in how much more does alternative tire "Y" weigh then OEM tire "X". If that variance is significant, likely it affects mpg. Could be hard to measure an mpg difference and attribute it to heavier tires, where oftentimes the alternative tire has a more aggressive tread pattern, a long recognized mpg depresser, and where oftentimes the alternative tire has a somewhat greater diameter which has an effect on final drive ratio, a sort of "overdrive" gearing effect.
From personal experience I know that significantly heavier, aggressively treaded, and taller tires has a material effect on handling, especially braking, due to the "flywheel effect" which the additional rotational mass provides. The first time I put a set of 11.00 x 33.00 Bandag recaps on my 1967 IH Scout 800, with 4 wheel drum brakes (with only faint power assist), I blew through the stoplight just a couple of blocks from the tire store: light went yellow, I got off the gas, applied the brakes, and nothing much happened. I penetrated the intersection before opposing traffic started off, but it was a real eye-opener!
Foy